This is an interesting question. My answer is that I think of this exercise as a rough kind of meta-analysis, where results are combined in a (weighted) arithmetic mean.
I think the reason geometric means don’t work well in these kinds of exercises is that there are all sorts or differences and errors in individual studies that make it very likely that some of them will show zero (or negative) effect. Once this happens your geometric mean goes to zero (or breaks). I don’t think it makes sense to say something like “if because of noise the effect size on one of my many studies happens to show 0% instead of 1%, my meta analysis effect should be 0% instead of 10%.”
Thanks for the thoughtful comment. I am a little torn about valuing pure intelligence effects. On one hand it seems silly to only focus on the income effect when we know that education likely increases intelligence, quality of democratic participation, socialization, wisdom, etc. but on the other hand, when I tried to find evidence for education increasing health or life satisfaction beyond what we would expect from the income effects, I did not find much (I mention this briefly towards the end of the post). I would want to be wiser and more intelligent partly because I would expect to be able to live a more satisfied life, and to be able to make better choices that would make me happier and healthier. If the additional intelligence doesn’t seem to be actually increasing heath or life satisfaction, it makes me more suspicious of the claim that it is really producing a valuable kind of intelligence or wisdom. On the other hand, I do believe that life satisfaction is only one of many morally valuable things. Maybe the (overly convenient) reconciliation of these intuitions is to say that health interventions likely have these other effects too, where a healthier person gains the ability to make more free decisions, and potentially live a more social and fuller life.